Thermoelectric devices are used for the conversion of thermal and electrical energy. They offer a number of advantages over competing technologies including scalability to small sizes and temperature differences, simple reliable designs and often low cost. However, they have not seen wide application in energy applications due to their limited conversion efficiency. This is a consequence of the limited performance of current thermoelectric materials, which can be characterized by a dimensionless figure of merit, ZT=σS2T/κ. There is no known fundamental limit on ZT. However, the combination of transport parameters entering ZT is a contradictory combination that does not occur in ordinary materials. Electronic structure plays a remarkably subtle role in thermoelectric performance that can however be simply visualized in terms of iso-energy surfaces. A long sought connection is drawn between topological insulators and high ZT thermoelectrics, explaining the overlap between these two interesting materials classes. Characteristics that can be used to identify new thermoelectric compositions are discussed and an efficient computational screening method based on an electronic fitness function is presented.